@Anna-Marie Hello, I would try two things. I assume that you use the Samsung messaging app. Access Settings / Applications and look for the Messages app. In the options, the three points on the top right, perform Uninstall updates, restart the phone and Update the Messages app manually. Check the app permissions.
If the problem persists: in Settings / Connections / Mobile networks / Access point names, the three dots on the top right-perform-Reset values.Reboot and check.Greetings.
@Anna-Marie: If your mother doesn't have access to a Mobile Data connection, then she won't be able to receive the MMS messages you send her. Further to the advice above, I recommend using WhatsApp, as this will allow you to send messages containing pictures and emojis over Wi-Fi. Your mum will need the app on her phone as well, but it's intuitive to use, and a great alternative to the standard Messages app.